Primordial cosmic complexity and effects of reheating

We study the effects of the reheating phase on the evolution of complexities for the primordial curvature perturbation using the squeezed formalism. We examine the evolution of the out-of-time correlator, the quantum discord, and circuit complexity, starting from the inflationary epoch to the radiation-dominated epoch with different reheating scenarios. We find that for a mode that reenters the horizon after reheating, the effect of a finite reheating epoch on the characteristic \textit{freeze-in} amplitude of these primordial complexities can only be distinguished up to three different classes depending on whether the equation of state parameter: $(i)$ $w_\mathrm{re}=1/3$ $(ii)$ $w_\mathrm{re}<1/3$, or, (iii) $w_\mathrm{re}>1/3$. For reheating with different EOS within these classes, the final amplitude will be the same -- hence, the detailed signature of reheating with a class on the complexity measures will be lost. Taking the central value of the scalar spectral index ($n_s=0.9649$) from Planck and the equation of state during reheating $w_\mathrm{re}=0.25$ as benchmark values, we found that the behavior of the complexities for all modes smaller than $1.27\times10^{16}\mathrm{Mpc^{-1}}$ can be classified as above. However, for the small-scale modes reentering the horizon during reheating, the signature of EOS on the evolution of these two complexities will be embedded in each of the cases separately.